The Construction of Locally D-Optimal Designs by Canonical Forms to an Extension for the Logistic Model

Abstract

Logistic regression models for binary response problems are present in a wide variety of industrial , biological, social and medical experiments; therefore, optimum designs are a valuable tool for experimenters, leading to estimators of parameters with minimum variance. Our interest in this contribution is to provide explicit formulae for the D-optimal designs as a function of the unknown parameters for the logistic model () () () () log , 1 , x x x q η θ η θ α β δ − = + + where q is an indicator variable. We have considered an experiment based on the dose-response to a fly insecticide in which males and females respond in different ways, proposed in Atkinson et al. (1995) [1]. To find the D-optimal designs, this problem has been reduced to a canonical form.